4. If the expression 25y^2 - 70y+d is a perfect square, where d is a constant, find the

value of d.

d = 49

Step-by-step explanation:

Given that the expression is a perfect square of the form

(ay - b) ² = a²y² - 2aby + b²

Then comparing like terms

a²y² = 25y², that is

a² = 25 ⇒ a = 5

and - 2aby = - 70y, thus

2ab = 70, that is

2 (5) b = 70

10b = 70 ⇒ b = 7

b² = 7² = 49

Hence

25y² - 70y + d = (5y - 7) ² = 25y² - 70y + 49

Thus d = 49